Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((C13⋊C9)⋊D13) |
| unambiguous semidirect product | (C13⋊C9)⋊D65 |
| derived, Hall | C5×C132 ⋊ C2×C9 |
| Hall | C5×C13×C13⋊C9 ⋊ C2 |
| Hall | C5⋊(C13⋊D13) ⋊ C9 |
| Hall | C13×C13⋊C9 ⋊ D5 |
| Sylow | C132 ⋊ C9×D5 |
| Sylow | C5 ⋊ (C13⋊C9)⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊((C13⋊C3)⋊D13) |
| commutator, hypocenter | C5×C132 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C132 | C2×C3 |
| prime radical | C3×C5⋊(C13⋊D13) | C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 585 |
Polycyclic presentation:
2,3,5,13^2,3|b^3=f,c^a=c^4,d^a=d^12,e^a=e^12,d^b=d^3696 conjugacy classes — view the full character table.
| maximal subgroup of | #44477645, #44477646, #44477647, … |
| maximal normal subgroup of | #44477645, #44477646, #44477647, … |
| maximal quotient of | #44477592, C2×C5⋊((C13⋊C9)⋊D13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 48);